as a weighted Ricci curvature for a geometric measure space. In fact, this tensor appeared earlier in work of Lichnerowicz [1]}. Volume comparison theorems for smooth metric measure spaces with \(\operatorname{Ric}_f\)  bounded from below have been established by Qian [2]}, Lott [3]}, Bakry–Qian [4]} and Wei–Wylie [5]}.
